Properties Of Functionally Graded Materials Research Articles

Love wave propagation in a smart composite structure of linear and exponential functionally graded porous piezoelectric material

Functionally graded materials (FGMs) have emerged as a promising avenue for enhancing the performance and longevity of surface acoustic wave (SAW) devices. This importance is gained due to gradual variation in functional properties of FGMs. In this paper, a mathematical model of a piezoelectric layer overlying a functionally graded porous piezoelectric (FGPP) layer resting on the elastic substrate is presented for the study of Love waves. The material parameters of the FGPP layer are considered to vary linearly and exponentially with the thickness of the layer. The solutions of governing equations corresponding to the FGPP layer are obtained by the Wentzel Kramers Brillouin (WKB) method. Dispersion equations are derived for both electrically open and shorted boundaries, linear and exponential gradation in both mechanical and electrical parameters, and for gradation in mechanical parameters alone as well. After numerical computation, dispersion curves are plotted to investigate the influence of wavenumber, type of gradation, extent of gradation, and type of boundaries on the phase and group velocity. The phase velocity decreases with wavenumber and is found more for linear gradation in comparison to exponential gradation. The electromechanical coupling factor is analyzed for different propagating modes of Love waves, in the case when gradation in mechanical properties is considered, the electromechanical coupling factor is greater than that when variation in both mechanical and electrical properties is considered. It is also observed that the tailoring of gradation can help to get the suitable value of the electromechanical coupling factor. The insights obtained from these findings can offer valuable contributions toward advancing the functionality and efficiency of SAW devices, there by bolstering their applicability in various technological domains.

Peridynamic differential operator for stress analysis of imperfect functionally graded porous sandwich beams based on refined zigzag theory

This study focuses on the stress analysis of imperfect functionally graded porous (FGP) sandwich beams using the Peridynamic Differential Operator (PDDO) and Refined Zigzag Theory (RZT). Functionally graded materials (FGMs) can be found in diverse engineering applications since they offer smooth transitions in the mechanical properties of distinct materials, unlike traditional composite materials. Micro-voids and porosities may appear inside the FGMs due to technical challenges during the manufacturing process of such materials. Therefore, understanding the stress variations of the FG sandwich beams with porosities/micro-voids, which are called imperfect FGMs, under loads is of vital importance. In order to achieve the porous configuration in the FG structures, the modified rule of mixtures is applied to calculate the effective material properties of FGMs. The RZT is very suitable for stress analysis of laminated composites, especially for thick and moderately thick beams. It contains only four kinematic variables and eliminates the use of the shear correction factors. In this study, the equilibrium equations of the RZT are solved by means of the PDDO for the stress analysis of imperfect FG sandwich beams having uniform and non-uniform porosity distributions. The PDDO transforms the differential equations into their nonlocal form, namely integral form, providing highly accurate approximations of the derivatives. A comprehensive PDDO analysis is performed for the investigation of the influence of the material variation, and even and uneven porosity distributions on the stress variations of the imperfect FG sandwich beams. It is noted that when the FG core exhibits soft material distributions, the effect of porosity is evident. The even type porosity distribution pattern is more influential on the axial displacement and stress variations in comparison with those of the uneven type porosity distribution pattern.

Printable functionally graded tibial implant for TAR: FE study comparing implant materials, FGM properties, and implant designs

Tibial implants with functionally graded material (FGM) for total ankle replacement (TAR) can provide stiffness similar to the host tibia bone. The FGM implants with low stiffness reduce stress shielding but may increase implant-bone micromotion. A trade-off between stress shielding and implant-bone micromotion is required if FGMs are to substitute traditionally used Ti and CoCr metal implants. The FGM properties such as material gradation law and volume fraction index may influence the performance of FGM implants. Along with the FGM properties, the design of FGM implants may also have a role to play. The objective of this study was to examine FGM tibial implants for TAR, by comparing implant materials, FGM properties, and implant designs. For this purpose, finite element analysis (FEA) was conducted on 3D FE models of the intact and the implanted tibia bone. The tibial implants were composed of CoCr and Ti, besides them, the FGM of Ti and HA was developed. The FGM implants were modelled using exponential, power, and sigmoid laws. Additionally, for power and sigmoid laws, different volume fraction indices were taken. The effect of implant design was observed by using keel type and stem type TAR fixation designs. The results indicated that FGM implants are better than traditional metal implants. The power law is most suitable for developing FGM implants because it reduces stress shielding. For both power law and sigmoid law, low values of the volume fraction index are preferrable. Therefore, FGM implant developed using power law with 0.1 vol fraction index is ideal with the lowest stress shielding and marginally increased implant-bone micromotion. FGM implants are more useful for keel type fixation design than stem type design. To conclude, with FGMs the major complication of stress shielding can be solved and the longevity and durability of TAR implants can be enhanced.

A numerical investigation for the development of functionally graded Ti/HA tibial implant for total ankle replacement: Influence of material gradation law and volume fraction index.

Stress shielding is one of the major concerns for total ankle replacement implants nowadays, because it is responsible for implant-induced bone resorption. The bone resorption contributes to the aseptic loosening and failure of ankle implants in later stages. To reduce the stress shielding, improvements can be made in the implant material by decreasing the elastic mismatch between the implant and the tibia bone. This study proposes a new functionally graded material (FGM) based tibial implant for minimizing the problem of stress shielding. Three-dimensional finite element (FE) models of the intact tibia and the implanted tibiae were created to study the influence of material gradation law and volume fraction index on stress shielding and implant-bone micromotion. Different implant materials were considered that is, cobalt-chromium, titanium (Ti), and FGM with Ti at the bottom and hydroxyapatite (HA) at the top. The FE models of FGM implants were generated by using different volume fractions and the rule of mixtures. The rule of mixtures was used to calculate the FGM properties based on the local volume fraction. The volume fraction was defined by using exponential, power, and sigmoid laws. For the power and sigmoid law varying volume fraction indices (0.1, 0.2, 0.5, 1, 2, and 5) were considered. The geometry resembling STAR® ankle system tibial implant was considered for the present study. The results indicate that FGMs lower stress shielding but also marginally increase implant-bone micromotion; however, the values were within the acceptable limit for bone ingrowth. It is observed that the material gradation law and volume fraction index influence the performance of FGM tibial implants. The tibial implant composed of FGM using power law with a volume fraction index of 0.1 was the preferred option because it showed the least stress shielding.

Effect of interdiffusion layer of functionally graded Al–Cu composites fabricated by spark plasma sintering on mechanical and thermal properties

The effect of the microstructure of multi-layer Al–Cu functionally graded materials (FGMs) fabricated through spark plasma sintering (SPS) on the mechanical and thermal properties was systemically investigated. Uniformly mixed Al–25, 50, 75 Cu (vol%) powder samples were prepared by mechanical ball milling and used for fabricating two types of FGMs: FGM 1 with three layers (Cu/Al–50Cu/Al) and FGM 2 with five layers (Cu/Al–75Cu/Al–50Cu/Al–25Cu/Al). These FGMs were then sintered at 400 °C under a compressive pressure of 250 MPa for 5 min. The microstructures of the sintered FGMs exhibited gradual variations in the Al and Cu contents. An interdiffusion layer composed of Cu9Al4 and CuAl2 at the layer/layer interfaces was observed, the thickness of which was analyzed by energy-dispersive spectroscopy line mapping. The Vickers hardness of FGM 1 and FGM 2 were higher than that calculated by rule of mixture due to the formation of Al–Cu IC such as Cu9Al4 and CuAl2. The drastic enhancement in a Al–75Cu layer was obtained by dominant formation of Cu9Al4. On the other hand, the thermal conductivity of the prepared FGMs was lower than that of Al due to the formation of Al–Cu ICs, enhanced heat dissipation compared with the Al–Cu composite materials. The mechanical and thermal properties of Al–Cu FGMs can be controlled by designing the layer composition or the number of layers.

Influence of laser power on mechanical properties of FGM of SS316L and IN625 fabricated by direct metal deposition

Direct Metal Deposition (DMD) is a metal Additive Manufacturing (AM) process. It is used for producing sustainability Functionally Graded Materials (FGM) and repairing of sophisticated parts. In this present research, a commercially available DMD machine deposited three partial FGM blocks of size 26 mm wide × 34 mm thick × 32 mm heights. The commonly influence parameters on Ultimate Tensile Strength (UTS) are scan velocity and laser power. The powders used for deposition were Stainless Steel 316L (SS316L), Inconel 625 (IN625), and their three different compositions. ASTM E8 tensile samples were cut from those blocks by wire cut-EDM. Micro-tensile tests were carried out on ASTM E8 samples using a SHIMADZU micro-tensile machine. The results revealed that partial FGM sample-2 had high sustainability UTS of 532 MPa as compared to remaining two samples. It is illustrated that for joining two dissimilar materials to obtain high UTS thick layered (i.e., thickness more than 1 mm) gradient path method should be selected at the medium laser power available on the DMD machine. However, the sample-3 has higher hardness at high laser power.

Dynamic analysis of functional gradient porous sigmoidal sandwich plates

Analysis of free vibrations of functionally graded (FG) porous sigmoid sandwich plates, is considered in this paper. The plate can have a complex geometric shape and various types of fastening. To solve the problem, we used the variational-structural method (RFM), which combines the theory of R-functions and variational method of Rayleigh-Ritz. The mathematical statement of the problem is carried out within the framework of the deformation theory of plates of the first order (FSDT). Plates are considered, the outer layers of which are made of functionally graded materials (FGM), and the core is isotropic. For different models of porosity distribution (sigmoid uniform and nonuniform), analytical expressions were obtained to calculate the effective properties of FGM. For rectangular plates, a comparison of the obtained results with known results obtained using other approaches is shown. Calculations for plates with a complex shape are presented in the form of tables and graphs. The influence of the volume fraction of ceramics, the different types Of FGM and the coefficient of porosity on the natural frequencies of the plate is analyzed.

Free vibration analysis of cracked composite plates reinforced with CNTs using extended finite element method (XFEM)

In this article, the free vibration behavior of cracked nanocomposite plates was investigated using the extended finite element method (XFEM), with a focus on examining the impact of different distribution patterns (UD, FG-X, FG-A, and FG-O) in the functionally graded (FG) carbon nanotube composite (FG-CNTRC) plate. The FG material properties are assumed to vary through the thickness direction according to different distributions. The governing equations are based on the first-order shear deformation plate theory (FSDT), and the nanocomposite plates are composed of a polymer matrix and the FG-CNTRC. The novelty of this article lies in studying the free vibration behavior of the CNTRC plate, considering all distribution patterns, using XFEM. The effective elastic modulus is computed using the modified Halpin Tsai model, while mass density and Poisson’s ratio are determined by employing the rule of mixture. A parametric study is conducted to investigate the effect of the crack length, crack position, width/thickness ratios, volume fraction, and power law index (Pin) of nanofillers on the natural frequencies of the CNTRC plate, offering valuable insights for different distribution patterns under various boundary conditions. The results demonstrate that the XFEM's accuracy and efficiency as a tool for the free vibration analysis of cracked nanocomposite plates.

A coupled hygro-elastic 3D model for steady-state analysis of functionally graded plates and shells

Abstract This 3D coupled hygro-elastic model proposes the three-dimensional (3D) equilibrium equations associated with the 3D Fick diffusion equation for spherical shells. The primary unknowns of the problem are the displacements and the moisture content. This coupled 3D exact shell model allows to understand the effects of the moisture field in relation with the elastic field on stresses and deformations in different plates and shells. This model is specifically developed for configurations including functionally graded material (FGM) layers. Four different geometries are analyzed using an orthogonal mixed curvilinear reference system. The main advantage of this reference system for spherical shells is the degeneration of the equations to those for simpler geometries. The solving method is the exponential matrix method in the thickness direction. The closed-form solution is possible because of simply supported sides and harmonic forms for displacements and moisture content. The moisture content amplitudes are directly applied at the top and bottom outer faces through steady-state hypotheses. The final system is based on a set of coupled homogeneous second-order differential equations. The moisture field effects are evaluated for the static analysis in terms of displacement, strain, and stress components. After preliminary validations, used to better understand how to properly define the calculation of the curvature-related terms and FGM properties, four new benchmarks are proposed for several thickness ratios, geometrical data, FGM configurations, and moisture values imposed at the external surfaces. From the results, it is clear the accordance between the uncoupled hygro-elastic model and this new coupled hygro-elastic model when the 3D Fick diffusion law is employed. Both effects connected with the thickness layer and the embedded material are included in the 3D hygro-elastic analyses proposed. The 3D coupled hygro-elastic model is simpler than the uncoupled one because the 3D Fick diffusion law does not have to be separately solved.

Nonlinear large-amplitude vibration analysis of annular sector plates made of FGMs subjected to cooling shock

A numerical approach is developed in the present article to study the geometrically nonlinear vibrations of annular sector plates made of functionally graded materials (FGMs) due to being exposed to cooling shock. The first-order shear deformation plate theory (FSDT) is used in the modeling of plate, and the governing equations of motion are derived based on Hamilton's principle considering von Kármán nonlinear kinematic relations. It is also considered that the properties of FGMs are dependent on temperature and distribution of materials. According to the uncoupled thermoelasticity theory, the temperature distribution is obtained via 1D Fourier-type transient heat conduction equation. To numerically solve the problem, the generalized differential quadrature (GDQ) method and Newmark-beta integration scheme are utilized. Considering two different types of thermal loading as cooling shock, the effects of various parameters including thermal load rapidity time, geometry, magnitude of thermal load and material properties on the large-amplitude vibrations of annular sector plates are investigated.

Topology optimization approach for functionally graded metamaterial components based on homogenization of mechanical variables

The micron resolutions that 3D printers are reaching allow for a change of paradigm in the design of components, optimizing not only the topology of the component, but also the microstructure of the material, which can adopt different objectives at different locations in the component, reaching different mechanical properties and different optimal microstructures at those locations. This constitutes a flip in the design objectives to focus on tailored material work, aimed either at local objectives or at component-wide ones, instead of pursuing homogeneous material properties for global objectives. For this new concurrent structure-material design leading to optimized components made of functionally graded (FG) metamaterials, new topology optimization (TO) procedures are needed in which the objective is to obtain component-wise mechanical variables or distributions of these variables, rather than global component objectives as compliance, which is a typical objective of classical TO approaches.In this work we present a new TO approach aimed at FG metamaterial design pursuing homogeneous mechanical variables. We focus on homogenization of deformation level along the component by minimizing its standard deviation across the domain. The proposed formulation can be naturally generalized to anisotropy, nonlinear behavior, and other optimization objectives. Convergence to a suitable optimized solution, with a distribution of material properties resulting in a homogeneously deformed component, is obtained. These FG material properties may be obtained from local metamaterial design. Classical material/void configurations may also be obtained following our procedure, and results for such cases can be compared qualitatively to the Solid Isotropic Material with Penalization (SIMP) approach.

Dynamic Analysis of Elastically Supported Functionally Graded Sandwich Beams Resting on Elastic Foundations Under Moving Loads

Vibration behaviors of elastically supported functionally graded (FG) sandwich beams resting on elastic foundations under moving loads are investigated. The transformed-section method is first applied to establish the bending vibration equations of FG sandwich beams, then the Chebyshev collocation method is used to study free and forced vibrations. Two types of sandwich beams with FG faces-isotropic core and isotropic faces-FG core are considered. The material properties of FG materials are assumed to vary across the beam thickness according to a simple power function. Regarding the free vibration analysis, bending vibration frequencies are calculated numerically by forming a matrix eigenvalue equation. As for the forced vibration analysis, the backward differentiation formula method is employed to solve the time-dependent ordinary differential equations to obtain the dynamic deformations of the beam. To ensure the accuracy of the proposed model, some calculated results are compared with those in the published literature. Parametric studies are then performed to demonstrate the effects of material gradient indexes, stack types, layer thickness ratios, slenderness ratios, excitation frequency and speed of moving loads, and foundation and support stiffness parameters on the dynamic characteristics of FG sandwich beams.

Transient thermoelastic fracture analysis of functionally graded materials using the scaled boundary finite element method

To model fracture in functionally graded materials (FGMs), the scaled boundary finite element method (SBFEM) is extended to examine the effects of fully coupled transient thermoelasticity. Previously developed SBFEM supplementary shape functions are utilized to model thermal stresses. The spatial variation of thermal and mechanical properties of FGMs are approximated by polynomial functions facilitating the semi-analytical evaluation of coefficient matrices. The dynamic stress intensity factors (SIFs) are also evaluated semi-analytically from their definitions without the need for additional post-processing. Scaled boundary polygon elements are employed to facilitate the meshing of complex crack geometries. Both isotropic and orthotropic materials with different material gradation functions are considered. To study the transient effects of thermoelasticity on fracture parameters, several numerical examples with different crack configurations and boundary conditions are considered. The current approach is validated by comparing the results of dynamic SIFs with available reference solutions.

Effect of porosity distribution on vibration and damping behavior of inhomogeneous curved sandwich beams with fractional derivative viscoelastic core

PurposeThe purpose of this paper is to parametrically investigate the vibration and damping characteristics of a functionally graded (FG) inhomogeneous and porous curved sandwich beam with a frequency-dependent viscoelastic core.Design/methodology/approachThe FG material properties in this study are assumed to vary through the beam thickness by power law distribution. Additionally, FG layers have porosities, which are analyzed individually in terms of even and uneven distributions. First, the equations of motion for the free vibration of the FG curved sandwich beam were derived by Hamilton's principle. Then, the generalized differential quadrature method (GDQM) was used to solve the resulting equations in the frequency domain. Validation of the proposed FG curved beam model and the reliability of the GDQ solution was provided via comparison with the results that already exist in the literature.FindingsA series of studies are carried out to understand the effects on the natural frequencies and modal loss factors of system parameters, i.e. beam thickness, porosity distribution, power law exponent and curvature on the vibration characteristics of an FG curved sandwich beam with a ten-parameter fractional derivative viscoelastic core material model.Originality/valueThis paper focuses on the vibration and damping characteristics of FG inhomogeneous and porous curved sandwich beam with frequency dependent viscoelastic core by GDQM – for the first time, to the best of the authors' knowledge. Moreover, it serves as a reference for future studies, especially as it shows that the effect of porosity distribution on the modal loss factor needs further investigation. GDQM can be useful in dynamic analysis of sandwich structures used in aerospace, automobile, marine and civil engineering applications.

Mechanical properties investigation of composite FGM fabricated from Al/Zn

AbstractThis article investigates the novel mechanical behavior of metal–metal gradients (Al/Zn) of the functionally graded materials (FGM) type. The experimental work includes the manufacture of three different models (FGM 1, FGM 2, and FGM 3) with various proportions of volume fraction and gradation as (100% Al–50% Al–50% Zn–50% Zn–50% Al–100% Zn), (100% Al–30% Zn–70% Al–70% Zn–30% Al–100% Zn) and (100% Al–70% Zn–30% Al–30% Zn–70% Al–100% Zn), respectively. The annealing process was carried out to eliminate the casting problems of the FGM. Mechanical tests such as tensile and hardness were performed using different parameters of the gradient of properties for each model. Hardness tests for each model were carried out by the circumferential method along the rod made of the FGM and in the radial direction from the core of the models and at different distances. In the third model, the modulus of elasticity and ultimate strength were 79 and 377 MPa, respectively. The densities of the three models were measured experimentally and theoretically. The results show that model FGM 3 has a tensile strength of 6, which is 10% more than that of models FGM 1 and FGM 2. The results showed a significant improvement of 22% in the tensile strength on average compared to the aluminum–zinc alloy. The circumferential method of hardness testing gives variant results than the radial type due to the properties of FGMs.

Review of thermoelastic, thermal properties and creep analysis of functionally graded cylindrical shell

ABSTRACT Functionally graded (FG) materials have shown excellent thermoelastic and creep performance, being considered as excellent materials for cylindrical shells subjected to thermo-mechanical loads. This review provides a detailed account of thermoelastic and creep properties of FG cylindrical shells. A review of governing equations on properties of FG materials as well as thermoelastic response of materials is provided. In depth analysis of the works carried out on the thermoelastic and creep performance of FG cylindrical under different thermal and mechanical loads (such as internal/external pressure, axial loading, etc.) is then conducted. Results obtained so far indicate the superior creep performance of FG cylindrical shells. Although many studies have been carried on thermoelastic response of FG cylindrical shells, their creep properties under different loading is yet to be extended and is a subject of interest for the future researches.

Fracture analysis of functionally graded material reinforced with MWCNT

Computational model based on extended isogeometric analysis is implemented for the fracture analysis of functionally graded material (FGM) reinforced with multi-walled carbon nanotube (MWCNT), i.e., FGM-MWCNT structure under mechanical and thermo-mechanical loading conditions. The FGM body taken for the study is composed of metal (Ti–6Al–4V) on the left side and ceramic (ZiO2) on right side. For the gradation of FGM properties that change throughout the domain length, exponential law is assumed. Moreover, the FGM is reinforced with 0–5% of MWCNT to obtain FGM-MWCNT composite. In order to perform this fracture analysis, first the equivalent mechanical and thermal properties of the FGM-MWCNT composite are evaluated using some of the micromechanics models cited in the literature. Using the interaction integral approach, SIFs are extracted. The results of the test show that when the volume percentage of MWCNTs increases, it enhances the failure resistance of the composite.

Functionally graded polyetheretherketone-based composites additively manufactured by material extrusion using a transition interface design method

The addition of short carbon fibers (CFs) and glass fibers (GFs) can significantly enhance the mechanical properties of polyetheretherketone (PEEK); however, ductility is significantly reduced. Owing to the significant differences in mechanical, thermal and tribological properties of CF/GF-PEEK, PEEK-based functionally graded materials (FGMs) are promising materials for 3D printing. This paper proposes a novel method for preparing FGMs using continuous welding filaments to improve the comprehensive performance of 3D printed CF/GF-PEEK. In addition, two innovative graded interface design methods are proposed for extrusion-based 3D printing of FGMs. Furthermore, a series of 3D printing experiments were conducted to verify our design methods. The 3D-printed FGMs composed of CF/GF-PEEK composites possess excellent toughness while maintaining good mechanical properties and interlayer bonding performance. The elongation at the fracture of the FGMs prepared in this study increased by 150% compared to those of fiber reinforced PEEK composites. The overall mechanical properties of FGMs with graded interfacial layers are improved by about 12% compared with those of the FGMs without transitional structures.

Elastoplastic Indentation Response of Sigmoid/Power Functionally Graded Ceramics Structures

Due to the applicability of new advanced functionally graded materials (FGMs) in numerous tribological systems, this manuscript aims to present computational and empirical indentation models to investigate the elastoplastic response of FG substrate under an indention process with spherical rigid punch. The spatial variation of the ceramic volume fraction through the specimen thickness is portrayed using the power law and sigmoid functions. The effective properties of two-constituent FGM are evaluated by employing a modified Tamura–Tomota–Ozawa (TTO) model. Bilinear hardening behavior is considered in the analysis. The finite element procedure is developed to predict the contact pressure, horizontal displacement, vertical deformation, and permanent deformation of FG structure under the rigid cylindrical indentation. The empirical forms for permanent deformation were evaluated and assigned. Model validation with experimental works was considered. The convergence of the mesh and solution procedure was checked. Numerical studies were performed to illustrate the influence of gradation function, gradation index, and indentation parameters on the contact pressure, von Mises stresses, horizontal/vertical displacements, and permanent plastic deformation. The present model can help engineers and designers in the selection of an optimum gradation function and gradation index based on their applications.

On the Vibration, Buckling and Dynamic Stability of Three-Directional Functionally Graded Circular Cylindrical Tubes with Consideration of Higher-Order Beam Theory

In view of engineered structures such as those of advanced aircraft and space shuttles are often required to withstand multidirectional loads. We present three-directional (3D) functionally graded materials (FGMs) to reconstruct circular cylindrical tubes placed on an elastic foundation, and the buckling, dynamic and stability behaviors are investigated. In contrast with those of unidirectional and bidirectional FGMs, the material properties of 3D FGMs are designed to vary continuously and smoothly in three directions to fulfill multifunctional requirements. Considering the higher-order beam theory, Hamilton’s principle is adopted to establish the governing equations with variable coefficients of the 3D FGMs tubes. The generalized differential quadrature method (GDQM) is used to predict the statics and dynamics. Numerical simulations are performed to obtain the effects of physical parameters, such as the 3D FGM indexes, on the natural frequency, buckling load and stability regions in detail. The results show that the mechanical behaviors of the circular cylindrical tubes can be easily tuned by introducing 3D FGMs, demonstrating that 3D FGMs have more potential than one-directional and two-directional FGMs in terms of improving the load-bearing capacity of structures and optimizing those structures.